Stable helical solitons in optical media

We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.     

A Lower Bound on the Partition Function for a Strictly Neutral Charge-Symmetric System

Journal of Statistical Physics - A lower bound on the grand partition function of a classical charge-symmetric system is adapted to the neutral grand canonical ensemble, in which the system is...     

A cognitively based simulation of academic science

The models used in social simulation to date have mostly been very simplistic cognitively, with little attention paid to the details of individual cognition. This work proposes a more cognitively realistic approach to social simulation. It begins with a model created by Gilbert (1997) for capturing the growth of academic science. Gilbert’s model, which was equation-based, is replaced here by an agent-based model, with the cognitive architecture CLARION providing greater cognitive realism. Using this cognitive agent model, results comparable to previous simulations and to human data are obtained. It is found that while different cognitive settings may affect the aggregate number of scientific articles produced, they do not generally lead to different distributions of number of articles per author. The paper concludes with a discussion of the correspondence between the model and the constructivist view of academic science. It is argued that using more cognitively realistic models in simulations may lead to novel insights. Isaac Naveh obtained a master’s degree in computer science at the University of Missouri. His research interests include hybrid cognitive models and multi-agent learning. Ron Sun is Professor of Cognitive Science at Rensselaer Polytechnic Institute, and formerly the James C. Dowell Professor of Engineering and Professor of Computer Science at University of Missouri-Columbia. He received his Ph.D in 1992 from Brandeis University. His research interest centers around studies of cognition, especially in the areas of cognitive architectures, human reasoning and learning, cognitive social simulation, and hybrid connectionist models. For his paper on integrating rule-based and connectionist models for accounting for human everyday reasoning, he received the 1991 David Marr Award from Cognitive Science Society. He is the founding co-editor-in-chief of the journal Cognitive Systems Research, and also serves on the editorial boards of many other journals. He is the general chair and program chair for CogSci 2006, and a member of the Governing Board of International Neural Networks Society. His URL is: http://www.cogsci.rpi.edu/~rsun     

Stabilization of nonlinear systems with a dither control

In this paper a new approach is taken to analyze stabilization of a general nonlinear system with a dither input. Given the original system with a control, an autonomous relaxed system is constructed. It is shown that if the relaxed system is stable, then the original system with dither control would be stable in the finite time. An algorithm is given for constructing the dither control. The technique used here is general and does not have the limitations of the Dual Input Describing Function technique. Furthermore, in many cases it is possible to guarantee global contractive stability as well. Two examples are solved in detail using computer simulations for demonstration of the technique.     

Theorems for conditional expectations,with applications to Markov processes

Several limit theorems analogous to Hopf’s ergodic theorem (but where the usual ratio is replaced by conditional expectation with respect to certain sigmafields) are proved and applications to probability theory are given.     

Polarization singularity democracy: WYSIWYG

The canonical point singularity of elliptically polarized light is a C point, an isolated point of circular polarization surrounded by a field of polarization ellipses. The defining singular property of a C point is that the surrounding ellipses rotate about the point. It is shown that this rotation is seen only for a particular line of sight (LOS) and, conversely, that there exists a unique LOS for every ellipse along which the ellipse is seen as a singularity. It is also shown that changes in LOS can turn singularities into stationary points and vice versa. The democratic behavior of polarization singularities and stationary points is a consequence of the fundamental "what you see is what you get" property of ellipse fields. Simple experiments are proposed for observing this unusual property of elliptically polarized light.     

Synthesis and studies of the properties of a liquid-crystalline quaterrylenebis(dicarboximide) by 1H NMR and UV-vis spectroscopies

The synthesis of an ionic quaterrylenebis(dicarboximide) 1a, a long-wavelength absorbing mesogen, is described. When compared with its analogue 2a, an ionic perylenebis(dicarboximide), the aromatic protons of 1a exchange with deuterium of concentrated D(2)SO(4) at a dramatically faster rate. In addition, stronger aggregation in aqueous media was observed for 1a.     

Synthesis of polymer dielectric layers for organic thin film transistors via surface-initiated ring-opening metathesis polymerization

The use of surface-initiated ring-opening metathesis polymerization (SI-ROMP) for producing polymer dielectric layers is reported. Surface tethering of the catalyst to Au or Si/SiO2 surfaces is accomplished via self-assembled monolayers of thiols or silanes containing reactive olefins. Subsequent SI-ROMP of norbornene can be conducted under mild conditions. Pentacene semiconducting layers and gold drain/source electrodes are deposited over these polymer dielectric films. The resulting field effect transistors display promising device characteristics, demonstrating for the first time that SI-ROMP can be used in the construction of organic thin-film electronic devices.     

On some transport properties of baker's maps

This paper considers the one-dimensional advection and diffusion of a passive scalar in the context of baker's maps of the unit interval. Our main interest is the thermal transport between two points held at fixed temperatures, when a deterministic sequence of maps of various scales are involved. Molecular diffusion occurs during the periods of rest between maps. We focus on the behavior of the transport in the limit of infinite Péclet number (or small molecular diffusion). Various asymptotic results are presented and compared with numerical calculations. Convergence to turbulent transport independent of molecular diffusion is observed as the number of scales is increased.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.